TY - JOUR
AU - Hall, Richard, J
AB - Abstract Individuals experience heterogeneous environmental conditions that can affect within-host processes such as immune defense against parasite infection. Variation among individuals in parasite shedding can cause some hosts to contribute disproportionately to population-level transmission, but we currently lack mechanistic theory that predicts when environmental conditions can result in large disease outbreaks through the formation of immunocompromised superspreading individuals. Here, I present a within-host model of a microparasite’s interaction with the immune system that links an individual host’s resource intake to its infectious period. For environmental scenarios driving population-level heterogeneity in resource intake (resource scarcity and resource subsidy relative to baseline availability), I generate a distribution of infectious periods and simulate epidemics on these heterogeneous populations. I find that resource scarcity can result in large epidemics through creation of superspreading individuals, while resource subsidies can reduce or prevent transmission of parasites close to their invasion threshold by homogenizing resource allocation to immune defense. Importantly, failure to account for heterogeneity in competence can result in under-prediction of outbreak size, especially when parasites are close to their invasion threshold. More generally, this framework suggests that differences in conditions experienced by individual hosts can lead to superspreading via differences in resource allocation to immune defense alone, even in the absence of other heterogeneites such as host contacts. Introduction Understanding how host responses to the external environment influence the progression of infection within hosts is a core aim in immunology. This is frequently quantified by experimental infection studies in response to an environmental treatment such as resource subsidy (Strandin et al. 2018) or light pollution (Kernbach et al. 2018). These treatment effects are then averaged over individuals within treatment groups, and used to quantify how typical infection loads change through time following infection (e.g., parasitemia curves; Komar et al. 2003; Handel and Rohani 2015). In natural systems, individuals experiencing similar environments may nonetheless exhibit substantial variation in components of their competence for infection, including contact behaviors, susceptibility, and intensity and duration of infection (Gervasi et al. 2015). Individuals exhibiting extreme values of one or more of these components can contribute disproportionately to infection transmission, a phenomenon known as superspreading (Lloyd-Smith et al. 2005); however, how intraspecific variation in competence arising from environmental conditions influences infection dynamics remains poorly understood. A key environmental factor shaping multiple dimensions of host–parasite interactions is availability of food resources. Seasonal food pulses, such as tree masting events, and anthropogenic activities that provide spatially reliable food resources, such as agriculture, landfills, and recreational feeding of wildlife, can aggregate individuals across the landscape and increase transmission risk through increased contact rates (Becker et al. 2015; Reil et al. 2015; Becker and Hall 2016), while low food availability can cause some or all individuals in a population to move away from transmission sites (Bartel et al. 2011; Brown and Hall 2018). At the individual level, food supplementation studies in wild and captive birds generally increase immune performance (reviewed in Strandin et al. 2018). Calorie restriction studies of captive wild-caught and laboratory-reared mammals have shown that moderate food restriction can temporarily enhance adaptive immunity (Lochmiller et al. 1993; Zysling et al. 2009; Eberhardt et al. 2013); however, severe food restriction tended to reduce immune performance, consistent with studies of wild-caught nestling birds hand-reared on a food-restricted diet (Brzek and Konarzewski 2007; Gutiérrez et al. 2011). Processes such as intraspecific competition, phenotypic variation in foraging efficiency, and patchiness of resources across the landscape can lead to individual variation in resource intake, which could be exacerbated or reduced by resource subsidy. However, whether variation in resource intake translates into sufficient variation in competence to influence outbreak size and duration at the population level is unknown (Altizer et al. 2018). Mathematical models provide a tool for quantifying the effects of environmental influences such as resource availability on infection dynamics both within and between hosts. Becker and Hall (2014) developed a simple model for how food subsidy influences infection dynamics in wildlife populations, finding that how host susceptibility responds to food intake critically determines whether food subsidy enhanced or reduced parasite transmission. However, the model did not incorporate within-host processes and was based on the heuristic assumption that host immune defense was an increasing, saturating function of food intake. Hite and Cressler (2018) coupled a population transmission model to a within-host model where host resource intake was split among maintenance, immune defense, and energy stolen by the parasite for replication. They showed that resource intake and virulence evolution could create emergent transmission dynamics not predicted by a population-level model alone, namely parasites riding resource-driven cycles of host abundance rather than suppressing these cycles. However, they related host infectiousness in the population model to the equilibrium parasite load of the within-host model, and thus this framework only applies to host–parasite systems where immune clearance of the pathogen is not possible. More sophisticated models of within-host dynamics, developed in concert with experimental infection studies, capture more details of parasite-immune system interactions, such as including a latent period for parasite-colonized cells (Banerjee et al. 2016) and multiple immune cell types associated with innate and adaptive responses (Handel et al. 2010). However, the additional number of parameters in these models presents challenges for discriminating among mechanistic hypotheses for the functional response of the immune system to infection or external processes. Similar to experimental studies, all of these models describe within-host processes in an “average” host, and thus the effects of among-host variation in resource intake and ensuing transmission dynamics at the population level remain unexplored. Here, I develop a simple model that mechanistically examines how changes in environmental resource availability influence resource-mediated immune functions which alter the duration of infection, and consequently, transmission among hosts. Thus, the model highlights how environmental variation can drive important heterogeneities in epidemiologically-relevant traits that are missed by classical models. As an example application of this framework, I simulate epidemics on host populations where heterogeneity in competence is generated by variation in resource intake, under scenarios of food scarcity and food subsidy relative to baseline availability. By comparing epidemic size in these heterogeneous models to mean field models based on average host resource intake, I quantify when food availability generates sufficient variation in competence to result in superspreading of infection. Model and methods The core components of the modeling framework, described in detail below (and summarized in Fig. 1) are (1) a within-host differential equation model for the interaction of the immune system and host cells targeted by a parasite; (2) the relationship between environmental resource availability and population-level variation in resource allocation to immunity; and (3) the population-level transmission model incorporating heterogeneity in infectious period. Fig. 1 Open in new tabDownload slide Schematic of the model structure for the within-host (left) and population-level transmission (right) models. Gray shading depicts the quantities influenced by resource availability that generates individual variation in resource intake and allocation. In the within-host model, host cells targeted by the parasite are uncolonized (⁠ U ⁠), parasite-colonized but not yet producing parasites (⁠ L ⁠) or parasite-producing (⁠ P ⁠). A host’s resource allocation to immunity (⁠ ρ ⁠) determines the number of immune cells generated (⁠ C ⁠) in response to detection of parasite-producing host cells; this immune response kills parasite-producing cells and reduces infection rates of new cells. The within-host model yields the host infectious period, defined as the time that the parasite-colonized cell density is above a transmission threshold. In the between-host transmission model, hosts are classified according to their infection status (Susceptible, S ⁠; Exposed, E ⁠; Infectious I ⁠; and Recovered R ⁠); heterogeneity in competence arises through resource-driven differences in the recovery rate (the inverse of the host infectious period). The effects of this heterogeneity are quantified by the outbreak size (the cumulative proportion of the population that becomes infected and recovers). Fig. 1 Open in new tabDownload slide Schematic of the model structure for the within-host (left) and population-level transmission (right) models. Gray shading depicts the quantities influenced by resource availability that generates individual variation in resource intake and allocation. In the within-host model, host cells targeted by the parasite are uncolonized (⁠ U ⁠), parasite-colonized but not yet producing parasites (⁠ L ⁠) or parasite-producing (⁠ P ⁠). A host’s resource allocation to immunity (⁠ ρ ⁠) determines the number of immune cells generated (⁠ C ⁠) in response to detection of parasite-producing host cells; this immune response kills parasite-producing cells and reduces infection rates of new cells. The within-host model yields the host infectious period, defined as the time that the parasite-colonized cell density is above a transmission threshold. In the between-host transmission model, hosts are classified according to their infection status (Susceptible, S ⁠; Exposed, E ⁠; Infectious I ⁠; and Recovered R ⁠); heterogeneity in competence arises through resource-driven differences in the recovery rate (the inverse of the host infectious period). The effects of this heterogeneity are quantified by the outbreak size (the cumulative proportion of the population that becomes infected and recovers). Within-host model I develop a model of an intracellular parasite and host immune response which is structurally similar to previous models of West Nile and influenza virus infection (Banerjee et al. 2016; Handel et al. 2010). Parasite-infectable host cells are categorized according to their infection status: uncolonized (⁠ U ⁠), parasite-colonized but not yet producing infectious stages (i.e., Latent, L ⁠), and parasite-colonized and producing new extracellular parasite stages (⁠ P ⁠). I make the simplifying assumption that extracellular infectious parasite stages produced are relatively short-lived compared to the duration of cell infection, and therefore that the density of infectious parasite stages is proportional to the current number of parasite-producing cells (⁠ P ⁠). Over the time course of infection, I ignore host replacement of parasite-infected host cells; a consequence of this assumption is that parasite replication is ultimately regulated by the supply of host cells even in the absence of a robust immune response (Banerjee et al. 2016), and therefore infections are guaranteed to be acute. I assume a simple mass action term for infection, so that the cellular infection rate is proportional to the number of uninfected and parasite-producing cells with rate constant b ⁠. Parasite-colonized cells move into the parasite-producing class at a constant rate g ⁠; unless first neutralized by the host immune response, parasite-infected cells die at rate d ⁠. I assume that the immune response can target the parasite in two ways: neutralizing free-living parasite stages, thus reducing the intracellular infection rate b (with parameter θ determining the strength of this reduction in relation to the number of immune cells generated); or killing parasite-producing cells in proportion to their encounter rate (the product of the parasite-producing and immune cell densities, with rate constant φ ⁠). I make the simplifying assumption that antibody-producing and killer cells are generated at similar rates in response to infection, and are limited by resource intake in similar ways; this allows me to track total immune cell production with a single variable C ⁠, similar to previous within-host models (Antia et al. 1994; Cressler et al. 2014). Production of new immune cells is initially in proportion to the killing rate of parasite-producing cells with rate constant a0 ⁠; however, to model the effect of resource-driven energetic constraints on the magnitude of the immune response, I assume that the total number of immune cells produced in response to infection, Cmax ⁠, is a linear function of host resources allocated to immune defense (⁠ ρ ⁠): Cmax=Cmin+αρ where Cmin is the minimum proliferative immune response under resource restriction and α is the maximum resource-driven increase in immune capacity. The equations describing this parasite-immune interaction are: dUdt=−bUP1+θCdLdt=bUP1+θC−gLdPdt=gL−dP−φCPdCdt=a0φCP(1−CCmax(ρ)) Environmental resource availability and variation in resources allocated to immune defense I assume that the distribution of resource intake across the host population, and therefore resource allocation to immune defense (⁠ ρ ⁠), follows a normal distribution; that is, ρ∼N(μ,σ2) ⁠. The distribution is truncated so that individuals in lower and upper tails of the distribution are assigned values of ρ=0 or ρ=1 ⁠, respectively. To relate different resource environments to the distribution of resource allocation to immunity, I assume that increasing the amount of resources available in the host’s habitat increases the mean and reduces the variance in resource intake across the population. In other words, all hosts are expected to increase their resource intake to similar levels in periods of high resource availability, through reduced intraspecific competition or increased encounter rates with resources, as observed in mammalian and bird populations capitalizing on anthropogenic food subsidies (Oro et al. 2013). Resource scarcity is assumed to cause reductions in individual intake, reflecting lower encounter rates, and higher intraspecific competition; food scarcity has also led to greater intraspecific variation in foraging strategies (Tinker et al. 2008) and success (via interference competition; Boyero and Pearson 2006). I explore the following resource availability scenarios: Baseline Under typical environmental conditions, I assume a mean resource allocation of 0.5 with a standard deviation (SD) of 0.15, so that 95% of the population has ρ values between 0.2 and 0.8. Resource scarcity For environments that are resource-poor relative to the baseline, the mean and SD of resource allocation are 0.3 and 0.2, respectively, so that 97.5% of the population has ρ values <0.7. Such conditions could occur naturally in harsh environmental conditions (e.g., drought or winter at high elevation or latitude), or due to anthropogenic land use change (e.g., logging and urbanization) that fragments and degrades habitat. Resource subsidy For resource-rich environments, the mean and SD of resource allocation are 0.7 and 0.1, respectively, so that 95% of the population has ρ values between 0.5 and 0.9. These could result from natural periods of resource abundance (e.g., tree masting and tropical rainy seasons), or from human activities that provide food subsidies for wildlife unintentionally (e.g., agriculture and landfills), or deliberately (e.g., recreation- or conservation-based feeding). Coupling within-host dynamics to a population-level transmission model To relate within-host dynamics to host competence for infection in the population model, I assume that parasite-colonized hosts are infectious when parasitemia is above a threshold value (Komar et al. 2003). Since I assume that free-living parasite stages are proportional to the density of parasite-producing cells, I define the host infectious period as the time that the parasite-producing cell density is above a critical threshold. Thus, for each value of resource allocation (⁠ ρ∈[0,1] ⁠), the within-host model generates a corresponding infectious period, InfPerρ ⁠. Since the relationship between peak parasitemia and the probability of between-host infection is context-dependent (Handel and Rohani 2015), I make the simplifying assumption that all hosts are equally infectious during their infectious period. To initiate the population-level transmission model for each resource availability scenario, I bin the host population into m(=5) equally-sized “competence” classes, so that each class contains 20% of the population in the 0–20th, 20th–40th (and so on) percentiles of the resource allocation distribution. Each competence class is assigned an infectious period corresponding to the value of ρ at the midpoint percentile for each class (i.e., the values of InfPerρ resulting from solving the within-host model for the 10th, 30th, 50th, 70th, and 90th percentile values of ρ ⁠). To focus on the effects of variation in immune performance resulting from environmental resource availability only, I make the following simplifying assumptions: Demography is unimportant over the timescale of the epidemic (i.e., no host births, deaths, or movements occur). Parasite infection is sub-lethal (i.e., there is no disease induced mortality). Recovered hosts remain immune to reinfection over the timescale of the epidemic. Contact rates, shedding rates, and susceptibility are all homogeneous across the population (so individuals differ only in their infectious periods). The rate at which hosts transition from exposed to infected is the same for all competence classes, since the density of parasite-producing cells always reaches the threshold for infectiousness before the immune response regulates pathogen replication. Note this is an emergent property of the within-host dynamics arising from two model assumptions. First, the assumption that immune cell proliferation depends on the density of parasite producing cells (P), but not parasite-colonized, latently infected cells (L), introduces an inherent delay in the immune response. Second, because I assumed resource intake primarily limits the carrying capacity of immune cell production, in the early stages of infection (i.e., when immune and parasite-producing cell densities are low), immune cell proliferation is largely unlimited by resources and is thus independent of ρ ⁠. The population model consists of 4m differential equations tracking the proportion of hosts according to their infection status (Susceptible, Exposed, Infectious, or Recovered) and competence (⁠ j=1:m ⁠). Transmission is density dependent with constant rate β ⁠, exposed individuals become infectious at rate λ and hosts recover from infection at a rate γj equal to the reciprocal of the infectious period for each class, that is, γj=1/InfPerj ⁠. The model equations are: dSjdt=−βSj∑j=1mIjdEjdt=βSj∑j=1mIj−λEjdIjdt=λEj−γjIjdRjdt=γjIj Model initiation and parameterization While not parameterized for a focal system, the default parameter values for the within-host dynamics are of the same order of magnitude as models parameterized from experimental infection of influenza (Handel et al. 2010) and West Nile Virus (Banerjee et al. 2016) in mouse models. For each of the environmental scenarios (baseline, resource restriction, and resource subsidy), the infectious period and initial proportion of individuals in each host competence class j was determined by solving the within host models and generating the corresponding infectious period distributions. The population model was solved numerically to determine current infection prevalence (⁠ ∑jIj ⁠) and cumulative outbreak size (⁠ ∑jRj ⁠) over time. To understand whether variation in infectious period generated by each environmental resource availability scenario had important effects on epidemic dynamics, I compared model outputs to those from a “homogeneous” SEIR model with a single competence class, where the recovery rate from infection, γ ⁠, is the reciprocal of the median infectious period. All epidemics were initiated by making a small fraction of individuals (1/1000th of total population size) infectious in the competence class corresponding to the median infectious period. All simulations were run in the R programming environment using the deSolve package, and code detailing the numerical solution of the within- and between-host models, and deriving the infectious period associated with the resource intake scenarios, is included as an Supplementary Appendix. Model parameters, definitions, and default values are listed in Table 1. Table 1 Definition of model parameters and initial conditions for resource availability scenarios, the within-host and between-host models, and their default values (or ranges explored in parentheses) Parameter Definition Value (range) Resource availability and allocation  ρ Resource allocation to host immune defense 0.5 (0–1)  Baseline Typical distribution of resource allocation in host population Mean = 0.5 SD = 0.15  Resource scarcity Distribution of resource intake under resource scarcity Mean = 0.3 SD = 0.2  Resource subsidy Distribution of resource intake under resource subsidy Mean = 0.7 SD = 0.1 Within host model  b Cellular infection rate 1 × 10−4  θ Reduction in infection rate through immune defense 1 × 10−3  g transition rate from parasite-colonized to parasite-producing 2.4  d Death rate of parasite-producing cells 3  φ Killing rate of parasite-producing cells by immune cells 1 × 10−3  a0 Maximum proliferation rate of immune cells in response to infected cell killing 2  Cmin Minimum capacity of immune cell production 500  α Additional capacity of immune cell production at maximum resource allocation 4500  IPcrit Threshold parasite-producing cell density above which host is capable of transmission 1000  U(0) Initial density of unparasitized cells 1 × 105  L(0) Initial density of parasite-colonized cells 1  P(0) Initial density of parasite-producing cells 0  C(0) Initial density of immune cells 1 Transmission model  β Transmission rate 0.45 (0.2–0.9)  λ Transition rate from exposed to infectious 0.26  InfPerj Infectious period of competence class j Model derived  γj Recovery rate of competence class j 1/InfPerj  Sj(0) Initial proportion of susceptible hosts in class j Model derived; sums to 0.999  Ej(0) Initial proportion of exposed hosts in class j 0  Ij(0) Initial proportion of infectious hosts in class j 0.001 (j = 3),0 otherwise  Rj(0) Initial proportion of recovered hosts in class j 0 Parameter Definition Value (range) Resource availability and allocation  ρ Resource allocation to host immune defense 0.5 (0–1)  Baseline Typical distribution of resource allocation in host population Mean = 0.5 SD = 0.15  Resource scarcity Distribution of resource intake under resource scarcity Mean = 0.3 SD = 0.2  Resource subsidy Distribution of resource intake under resource subsidy Mean = 0.7 SD = 0.1 Within host model  b Cellular infection rate 1 × 10−4  θ Reduction in infection rate through immune defense 1 × 10−3  g transition rate from parasite-colonized to parasite-producing 2.4  d Death rate of parasite-producing cells 3  φ Killing rate of parasite-producing cells by immune cells 1 × 10−3  a0 Maximum proliferation rate of immune cells in response to infected cell killing 2  Cmin Minimum capacity of immune cell production 500  α Additional capacity of immune cell production at maximum resource allocation 4500  IPcrit Threshold parasite-producing cell density above which host is capable of transmission 1000  U(0) Initial density of unparasitized cells 1 × 105  L(0) Initial density of parasite-colonized cells 1  P(0) Initial density of parasite-producing cells 0  C(0) Initial density of immune cells 1 Transmission model  β Transmission rate 0.45 (0.2–0.9)  λ Transition rate from exposed to infectious 0.26  InfPerj Infectious period of competence class j Model derived  γj Recovery rate of competence class j 1/InfPerj  Sj(0) Initial proportion of susceptible hosts in class j Model derived; sums to 0.999  Ej(0) Initial proportion of exposed hosts in class j 0  Ij(0) Initial proportion of infectious hosts in class j 0.001 (j = 3),0 otherwise  Rj(0) Initial proportion of recovered hosts in class j 0 Open in new tab Table 1 Definition of model parameters and initial conditions for resource availability scenarios, the within-host and between-host models, and their default values (or ranges explored in parentheses) Parameter Definition Value (range) Resource availability and allocation  ρ Resource allocation to host immune defense 0.5 (0–1)  Baseline Typical distribution of resource allocation in host population Mean = 0.5 SD = 0.15  Resource scarcity Distribution of resource intake under resource scarcity Mean = 0.3 SD = 0.2  Resource subsidy Distribution of resource intake under resource subsidy Mean = 0.7 SD = 0.1 Within host model  b Cellular infection rate 1 × 10−4  θ Reduction in infection rate through immune defense 1 × 10−3  g transition rate from parasite-colonized to parasite-producing 2.4  d Death rate of parasite-producing cells 3  φ Killing rate of parasite-producing cells by immune cells 1 × 10−3  a0 Maximum proliferation rate of immune cells in response to infected cell killing 2  Cmin Minimum capacity of immune cell production 500  α Additional capacity of immune cell production at maximum resource allocation 4500  IPcrit Threshold parasite-producing cell density above which host is capable of transmission 1000  U(0) Initial density of unparasitized cells 1 × 105  L(0) Initial density of parasite-colonized cells 1  P(0) Initial density of parasite-producing cells 0  C(0) Initial density of immune cells 1 Transmission model  β Transmission rate 0.45 (0.2–0.9)  λ Transition rate from exposed to infectious 0.26  InfPerj Infectious period of competence class j Model derived  γj Recovery rate of competence class j 1/InfPerj  Sj(0) Initial proportion of susceptible hosts in class j Model derived; sums to 0.999  Ej(0) Initial proportion of exposed hosts in class j 0  Ij(0) Initial proportion of infectious hosts in class j 0.001 (j = 3),0 otherwise  Rj(0) Initial proportion of recovered hosts in class j 0 Parameter Definition Value (range) Resource availability and allocation  ρ Resource allocation to host immune defense 0.5 (0–1)  Baseline Typical distribution of resource allocation in host population Mean = 0.5 SD = 0.15  Resource scarcity Distribution of resource intake under resource scarcity Mean = 0.3 SD = 0.2  Resource subsidy Distribution of resource intake under resource subsidy Mean = 0.7 SD = 0.1 Within host model  b Cellular infection rate 1 × 10−4  θ Reduction in infection rate through immune defense 1 × 10−3  g transition rate from parasite-colonized to parasite-producing 2.4  d Death rate of parasite-producing cells 3  φ Killing rate of parasite-producing cells by immune cells 1 × 10−3  a0 Maximum proliferation rate of immune cells in response to infected cell killing 2  Cmin Minimum capacity of immune cell production 500  α Additional capacity of immune cell production at maximum resource allocation 4500  IPcrit Threshold parasite-producing cell density above which host is capable of transmission 1000  U(0) Initial density of unparasitized cells 1 × 105  L(0) Initial density of parasite-colonized cells 1  P(0) Initial density of parasite-producing cells 0  C(0) Initial density of immune cells 1 Transmission model  β Transmission rate 0.45 (0.2–0.9)  λ Transition rate from exposed to infectious 0.26  InfPerj Infectious period of competence class j Model derived  γj Recovery rate of competence class j 1/InfPerj  Sj(0) Initial proportion of susceptible hosts in class j Model derived; sums to 0.999  Ej(0) Initial proportion of exposed hosts in class j 0  Ij(0) Initial proportion of infectious hosts in class j 0.001 (j = 3),0 otherwise  Rj(0) Initial proportion of recovered hosts in class j 0 Open in new tab Results Within-host dynamics The interaction of the immune system and the parasite produces an asymmetric hump-shaped curve for the density of parasite-producing cells over time (Fig. 2a). An initially rapid proliferation of infected cells is followed by a slower decline in infected cell density; the rate of this decline increases with resources allocated to immune defense (⁠ ρ ⁠). The host infectious period (defined as the time for which the density of parasite-producing host cells is above a threshold) is a nonlinear decreasing function of resources allocated to immune defense (Fig. 2b). For this parameterization, the infectious period under standard resource allocation (⁠ ρ=0.5 ⁠) is 2.34 days, and ranges from 4.77 days (minimum immune response, ρ=0 ⁠) to 1.87 days (maximum immune response, ρ=1 ⁠). Thus, reducing resource allocation to immune defense causes proportionately larger increases to the infectious period than the proportionate decrease in infectious period from increasing allocation. Fig. 2 Open in new tabDownload slide (a) The number of parasite producing infected cells through time under three levels of resource allocation to immunity (⁠ ρ ⁠): minimum allocation (⁠ ρ=0 ⁠, thin line), typical allocation (⁠ ρ=0.5 ⁠, standard line width) and maximum allocation (⁠ ρ=1 ⁠, thick line). The dashed line indicates the threshold cell density (⁠ 103 ⁠) above which the host is considered capable of transmitting infection; the time for which each curve is above this line represents the infectious period. (b) Host infectious period as a function of resources allocated to immune defense (⁠ ρ ⁠). Additional parameter values are given in Table 1. Fig. 2 Open in new tabDownload slide (a) The number of parasite producing infected cells through time under three levels of resource allocation to immunity (⁠ ρ ⁠): minimum allocation (⁠ ρ=0 ⁠, thin line), typical allocation (⁠ ρ=0.5 ⁠, standard line width) and maximum allocation (⁠ ρ=1 ⁠, thick line). The dashed line indicates the threshold cell density (⁠ 103 ⁠) above which the host is considered capable of transmitting infection; the time for which each curve is above this line represents the infectious period. (b) Host infectious period as a function of resources allocated to immune defense (⁠ ρ ⁠). Additional parameter values are given in Table 1. Resource availability and variation in host competence For each resource availability scenario, the frequency distribution of resource allocation to immunity in the host population followed a truncated normal distribution. Relative to the baseline scenario (centered on ρ=0.5 ⁠), the resource scarcity scenario had a lower mean and higher variance in resource allocation to immunity, so that just over 6% of the population was maximally competent for infection, while under resource subsidy the the mean resource allocation to immunity was higher and the variance was lower (Fig. 3a). The associated infectious period distributions were all right-skewed (Fig. 3b); the baseline scenario yielded a median infectious period of 2.34 (inter-quartile range 2.19–2.58 days), resource scarcity increased the median (2.89) and inter-quartile range (2.48–3.74), and resource subsidy reduced the median (2.09) and inter-quartile range (2.02–2.15). Fig. 3 Open in new tabDownload slide In all of the following figures, the line colors refer to the three environmental resource availability scenarios: baseline (black), resource scarcity (red) and resource subsidy (blue). The frequency distribution of (a) resource allocation to immunity (⁠ ρ ⁠) and (b) infectious period in the host population. Transmission model output of (c) infection prevalence (i.e., the proportion of the host population that is currently infectious) and (d) cumulative outbreak size (i.e., the proportion recovered from infection) through time, comparing models where heterogeneity in host competence is included (solid lines) or ignored (dashed lines). The transmission rate (⁠ β=0.45 ⁠) is chosen so that the parasite is just above its transmission threshold (⁠ R0=1.05 ⁠) under baseline resource availability in the homogeneous model (black dashed line). Sensitivity to the parasite transmission rate (⁠ β ⁠) of (e) final outbreak size in the heterogeneous (bold lines) and homogeneous (dashed lines) models, and (f) the difference in outbreak size between these models. Fig. 3 Open in new tabDownload slide In all of the following figures, the line colors refer to the three environmental resource availability scenarios: baseline (black), resource scarcity (red) and resource subsidy (blue). The frequency distribution of (a) resource allocation to immunity (⁠ ρ ⁠) and (b) infectious period in the host population. Transmission model output of (c) infection prevalence (i.e., the proportion of the host population that is currently infectious) and (d) cumulative outbreak size (i.e., the proportion recovered from infection) through time, comparing models where heterogeneity in host competence is included (solid lines) or ignored (dashed lines). The transmission rate (⁠ β=0.45 ⁠) is chosen so that the parasite is just above its transmission threshold (⁠ R0=1.05 ⁠) under baseline resource availability in the homogeneous model (black dashed line). Sensitivity to the parasite transmission rate (⁠ β ⁠) of (e) final outbreak size in the heterogeneous (bold lines) and homogeneous (dashed lines) models, and (f) the difference in outbreak size between these models. Consequences of resource-driven variation in competence for transmission In order to assess whether heterogeneity in competence can alter parasite invasion potential, I fixed the transmission rate (⁠ β ⁠) so that the pathogen’s basic reproductive number (⁠ R0 ⁠) is just above the invasion threshold when heterogeneity in competence is ignored in the baseline resource availability scenario. I then compared current infection prevalence (Fig. 3c) and cumulative outbreak size (Fig. 3d) over time in the heterogeneous competence model versus the homogeneous model for each of the environmental resource availability scenarios. For the baseline scenario, peak infection prevalence was slightly higher when heterogeneity in infectious period resulting from food intake was accounted for, and overall 5% more of the population was infected over the course of the outbreak. Relative to this baseline, resource scarcity resulted in higher peak prevalence and final outbreak size, and faster epidemic turnover. Accounting for heterogeneity in competence under resource scarcity yielded pronounced differences in epidemic dynamics, with higher peak prevalence (peaking slightly earlier) and 11% more of the population eventually infected, relative to the homogeneous model. Under resource subsidy, no outbreak occurred in either the heterogeneous or homogeneous model. When the parasite transmission rate was varied, resource scarcity that reduces immune performance allows parasites to invade at lower transmission rates, and cause larger outbreaks, relative to baseline availability, while resource subsidy has the opposite effect (Fig. 3e). For each resource scenario, the largest differences in outbreak size between the heterogeneous and homogeneous models occur at the invasion threshold for transmission in the homogeneous model (Fig. 3f). For this model parameterization, the peak difference in outbreak size was 13% for the resource scarcity scenario, 5% for the baseline, and <1% for resource subsidy. Discussion How organisms interact with their external environment can shape individual host responses to infection, and population-level variation in competence for infection, but integrating environmentally-driven immunological differences into transmission models is complex. The modeling framework developed in this paper is an initial attempt to bridge within-host and between-host processes, by quantifying how one component of competence that is often treated as fixed in population models, the host infectious period, is the outcome of interactions between resource-dependent immune defense and internal parasite replication. This framework permits exploration of how variation among individuals related to their environment (in this case, resource intake and allocation) produces variation in competence, and when this variation in competence is an important determinant of epidemic dynamics. This study suggests that conditions of resource scarcity can generate superspreading individuals, where a lack of resources allocated to immune defense causes them to be infectious for longer. Conversely, resource subsidy could reduce outbreak potential and size by “leveling the playing field” and allowing all individuals to invest in immune response. Prior models have explicitly coupled within-host and between-host transmission dynamics, often in the context of understanding virulence evolution (Mideo et al. 2008) and emergence of drug resistance (Webb et al. 2005). An outstanding question in bridging these scales is how intensity of infection scales to influence the between host transmission rate (Handel and Rohani 2015). Some studies have employed a “separation of timescales” argument to relate equilibrium parasite load to the transmission rate and assume lifelong infection (Hite and Cressler 2018). Instead, I focused on the duration of infection as an emergent property of the parasite-immune system interaction, dependent on the empirically supported idea of a parasitemia threshold (Komar et al. 2003). In the parameterization I used, all hosts exposed to the parasite became infected; however, a stronger immune response (or an elevated transmission threshold) would allow for the case of low-intensity infections that are quashed by the immune system; environmental conditions that favor such “resistant” individuals could reduce the population risk of pathogen invasion. Past work on superspreading has hypothesized, or presented empirical evidence for, variation in one or more components of host competence, such as variable shedding rates (Matthews et al. 2006) or contact rates among individuals or groups (Woolhouse et al. 2005; Craft 2015). This variation is then incorporated into stochastic and individual-based epidemiological models to demonstrate how superspreaders elevate transmission potential or outbreak size (Galvani and May 2005). Similar to findings of this study, chronically infected superspreaders with long infectious periods can facilitate disease persistence in pathogens exhibiting different courses of infection among hosts (Kramer-Schadt et al. 2009). To date, most models of superspreading do not explore the within-host mechanisms that generate variation in competence. The modeling framework presented here attempts to bridge this gap, and demonstrates how even symmetrical population-level variation in a key trait, resource intake, can result in a skewed distribution of infectious periods where 20% of highly-competent hosts can cause dramatic differences in outbreak size under standard or resource-restricted conditions. For simplicity, I developed a deterministic transmission model by binning individuals into a small number of competence classes; however, since this approach allows a continuous distribution of infectious periods to be generated, it would be straightforward to develop individual-based transmission models where individuals’ infectious periods are sampled from this distribution. A key assumption linking the external environment to internal parasite-immune dynamics was that resources (up to a point) increase the capacity of the immune system to respond to infection. While there is substantial empirical support for this, especially in food subsidized birds (Strandin et al. 2018), there is evidence from food restriction studies that components of immune performance improve with reduced resource intake in some mammals (Lochmiller et al. 1993). Indeed, it has been suggested that some animals reduce food intake in response to infection, to “starve the parasite,” or temporarily upregulate immune defense (Kyriazakis et al. 1998; Adelman and Martin 2009). More sophisticated within-host models, that include tradeoff mechanisms when host energy is split between immune defense, host maintenance, and parasite replication (e.g., Cressler et al. 2014), could be used to explore the drivers and consequences of nonlinear relationships between resource intake and immunity. Mirroring past theoretical work (Becker and Hall 2014), this study suggests that increasing food availability can reduce parasite transmission through resource-driven improvements to immune defense. Synthetic reviews (Murray et al. 2016) and meta-analysis (Becker et al. 2015) of the effects of anthropogenic food subsidy on wildlife disease show mixed support for this hypothesis, and many examples of where the opposite pattern (i.e., increased infection in food-subsidized populations) is observed. One potential mechanism for this disparity is covariation of other components of host competence, such as intraspecific contact rates, that could increase with food availability (e.g., if animals aggregate at feeding stations; Adelman et al. 2015). Although not explored here, this model framework is readily extendable to associate demographic or behavioral parameters with environmental resource availability. From an immunological perspective, ignoring these population-level factors that shape exposure to pathogens could lead to incorrect interpretation of experimental infection studies in the context of transmission risk. Constraints on replication in field and experimental studies mean that the effects of food availability and other environmental factors on individual variation in host competence are understudied. This study found that when food scarcity increases variation in resource intake among individuals, the ensuing generation of immunocompromised superspreaders increases outbreak risk, while resource subsidy that reduces variation in competence can prevent outbreaks. This suggests that extrapolating population-averaged immune metrics to seasons where resources are scarce or plentiful, or where human activity permanently degrades or improves access to resources, may lead to incorrect predictions about outbreak potential. An important caveat is that my model assumed no behavioral or fitness consequences of infection or immunity, which could reduce variation in competence if mounting a strong immune defense, or experiencing sustained, high-intensity infection, results in host mortality (Graham et al. 2011), or enhance the potential for superspreading if sickness behaviors enhance transmission risk (Bouwman and Hawley 2010) . Thus, future studies of how environmental conditions influence covariation of immunological, physiological, and behavioral components of host competence among individuals are a vital next step for furthering understanding of infection patterns in heterogeneous populations. Acknowledgments The author thanks Sonia Altizer, Vanessa Ezenwa, and Andrew Park for helpful discussions, and gratefully acknowledges support from the Division of Ecoimmunology and Disease Ecology, Division of Comparative Endocrinology, Division of Animal Behavior, and Division of Ecology and Evolution of the Society for Integrative and Comparative Biology, as well as the Macroecology of Infectious Disease Research Coordination Network funded by the National Science Foundation (NSF DEB 1316223), for supporting the symposium “The Scale of Sickness: How Immune Variation across Space and Species Affects Infectious Disease Dynamics” financially. Funding This work was supported by the National Science Foundation (NSF DEB 1518611). Supplementary data Supplementary data available at ICB online. References Adelman JS , Martin LB. 2009 . Vertebrate sickness behaviors: adaptive and integrated neuroendocrine immune responses . Integr Comp Biol 49 : 202 – 14 . 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TI - Modeling the Effects of Resource-Driven Immune Defense on Parasite Transmission in Heterogeneous Host Populations
JF - Integrative and Comparative Biology
DO - 10.1093/icb/icz074
DA - 2019-11-01
UR - https://www.deepdyve.com/lp/oxford-university-press/modeling-the-effects-of-resource-driven-immune-defense-on-parasite-ko9VRD0c4f
SP - 1253
VL - 59
IS - 5
DP - DeepDyve
ER -